1. Using a slotted spoon, remove the tomatoes from their cooking syrup (reserving the syrup). Place the tomatoes in a large, heavy saucepan and mash to a fine pulp with a potato masher. Turn the heat to medium and reduce the pulp to the thickness of tomato paste, stirring constantly so it doesn’t burn. Measure out 1¼ cups. Reserve the rest for spreading on toast. Return the measured amount to the saucepan.

2. Whisk the cream, half-and-half and vanilla into the pulp and place over medium heat. Stir constantly to prevent scorching. When the mixture reaches a simmer — do not let it boil — turn off the heat. Set aside to infuse for 10 to 15 minutes.

3. Meanwhile, in a medium bowl, whisk together the egg yolks and the sugar. Whisk about 1 cup of the hot cream into the egg yolks, then return this mixture to the remaining hot cream. Stir over medium-low heat until the custard reaches 180 degrees on a candy thermometer or thickly coats the back of a spoon, then remove from the heat. The custard should be thick and creamy, similar to egg nog.

4. Half-fill a large bowl with ice water. Strain custard into a smaller bowl. Rest the smaller bowl in the ice bath and let cool, stirring often. Chill.

6. To serve, make a caramel syrup if you like: In a small saucepan, combine the sugar and lemon juice with 1 tablespoon water. Cook over medium-high heat until the sugar caramelizes to a dark amber color. Remove from the heat and let cool for 1 minute. Whisk in the cream, then 3 tablespoons of the reserved tomato syrup. Scoop the ice cream into bowls and drizzle with a little caramel tomato syrup. Makes 1½ quarts.